To solve for the average rate of change of the function $f(x)$ between $x = 3$ and $x = 7$, we use the following formula:

$\text{Average Rate of Change} = \frac{f(7) - f(3)}{7 - 3}$

From the graph:

• The value of $f(3)$ is approximately $1.5$.
• The value of $f(7)$ is approximately $5.5$.

Substituting these into the formula:

$\text{Average Rate of Change} = \frac{5.5 - 1.5}{7 - 3} = \frac{4}{4} = 1$

So, the average rate of change is 1.

Would you like any further clarification or more details on this? Here are a few related questions you could explore:

1. How would you find the instantaneous rate of change at $x = 5$?
2. What does the sign of the average rate of change tell us about the function?
3. Could you estimate the average rate of change from $x = 2$ to $x = 6$?
4. What would happen if $f(7)$ was lower than $f(3)$? How would that affect the rate?
5. How can we calculate the slope between any two points on a graph?

Tip: The average rate of change is essentially the slope between two points on the graph, often interpreted as the "overall" trend of the function between those points.